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Exponent of a finite group admitting a coprime automorphism of prime order

  • Sara Rodrigues and Pavel Shumyatsky EMAIL logo
From the journal Journal of Group Theory

Abstract

Let 𝐺 be a finite group admitting an automorphism 𝜙 of prime order 𝑝 such that (|G|,p)=1. It is shown that if the fixed-point subgroup for 𝜙 has rank 𝑟 and (x-1xϕ)e=1 for each xG, then the exponent of [G,ϕ] is (e,p,r)-bounded.

Funding statement: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Apoio à Pesquisa do Distrito Federal (FAPDF), Brazil.

  1. Communicated by: Evgenii I. Khukhro

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Received: 2020-09-10
Revised: 2020-11-16
Published Online: 2020-12-09
Published in Print: 2021-05-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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